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A146212
Number of intersection points of all lines through the vertices of a regular n-gon.
16
3, 5, 15, 37, 91, 145, 333, 471, 891, 901, 1963, 2185, 3795, 3969, 6681, 5563, 10963, 11141, 17031, 17293, 25323, 21913, 36325, 36479, 50571, 50485, 68643, 51661, 91171, 90753, 118833, 118355, 152355, 139861, 192511, 191445, 240123, 238481
OFFSET
3,1
COMMENTS
This includes intersection points outside of the n-gon. Note that for odd n, n divides a(n); for even n, n divides a(n)-1. For odd n, it appears that a(n)=n(n^3-7n^2+15n-1)/8.
That formula is correct: see the Sidorenko link. - N. J. A. Sloane, Sep 12 2021
LINKS
Scott R. Shannon, Image for n = 3. In this and other images the dots showing the regular n-gon's vertices are slightly larger and circled with white for clarity. The dot color key is at the top-left of the image.
Scott R. Shannon, Image for n = 4.
Scott R. Shannon, Image for n = 5.
Scott R. Shannon, Image for n = 6.
Scott R. Shannon, Image for n = 7.
Scott R. Shannon, Image for n = 8.
Scott R. Shannon, Image for n = 9.
Scott R. Shannon, Image for n = 10.
Scott R. Shannon, Image for n = 11.
Scott R. Shannon, Image for n = 12.
FORMULA
There is a formula for odd n: see Comment section and the Sidorenko link. - N. J. A. Sloane, Sep 12 2021
EXAMPLE
a(5)=15 because there are 5 points inside the pentagon, 5 points on the pentagon and five points outside of the pentagon.
CROSSREFS
Bisection: A347319, A347321.
Sequence in context: A295614 A089485 A279684 * A265762 A018516 A138017
KEYWORD
nice,nonn
AUTHOR
T. D. Noe, Oct 28 2008
EXTENSIONS
More terms from Jon E. Schoenfield, Nov 10 2008
STATUS
approved